A Measure for the Vulnerability of Uniform Hypergraph Networks: Scattering Number

Ning Zhao, Haixing Zhao () and Yinkui Li
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Ning Zhao: School of Computer, Qinghai Normal University, Xining 810000, China
Haixing Zhao: School of Computer, Qinghai Normal University, Xining 810000, China
Yinkui Li: School of Mathematics and Statistics, Qinghai Minzu University, Xining 810000, China

Mathematics, 2024, vol. 12, issue 4, 1-11

Abstract: The scattering number of a graph G is defined as s ( G ) = m a x { ω ( G − X ) − | X | : X ⊂ V ( G ) , ω ( G − X ) > 1 } , where X is a cut set of G , and ω ( G − X ) denotes the number of components in G − X , which can be used to measure the vulnerability of network G . In this paper, we generalize this parameter to a hypergraph to measure the vulnerability of uniform hypergraph networks. Firstly, some bounds on the scattering number are given. Secondly, the relations of scattering number between a complete k -uniform hypergraph and complete bipartite k -uniform hypergraph are discussed.

Keywords: scattering number; complete k-uniform hypergraph; complete bipartite k-uniform hypergraph; dual hypergraph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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